Rearranging an equation using log functions

Hi guys. I'm trying to rearrage an equation using the natural log and I thought I had it correct but am now struggling. I need to rearange it into the form: y=a0 + a1*C. Where a0 and a1 are some combination of the other variables and numbers below

2. Relevant equations

H = ((2^(X-1))-1)/(K*(X-1)*C^(X-1))

H,X,K and C are all variables

3. The attempt at a solution

I've tried rearanging using log laws but I now think it might be wrong.

ln(H) = ln(2^(X-1)-1) - ln(K*(X-1)) - (X-1)*ln(C)

But I'm not sure if this is legal considering the equation could be rearranged to:

ln(H) = ln(2^(X-1)-1) - ln(K*(X-1)) - (X-1)*ln(C)
H = (2^(X-1))/(K*(X-1)*C^(X-1)) - 1/(K*(X-1)*C^(X-1))
These two are fine. But
ln(H) = ln(2^(X-1))/(K*(X-1)*C^(X-1)) - ln(1/(K*(X-1)*C^(X-1)))
Is not right. You can only apply log once to each side (as you said), it would be:
ln(H) = ln((2^(X-1))/(K*(X-1)*C^(X-1))- 1/(K*(X-1)*C^(X-1)))

But What is it you are trying to do? Get C to be the subject of the equation?